A multiscale approach to estimating topographically correlated propagation delays in radar interferograms

Abstract

[1] When targeting small amplitude surface deformation, using repeat orbit Interferometric Synthetic Aperture Radar (InSAR) observations can be plagued by propagation delays, some of which correlate with topographic variations. These topographically-correlated delays result from temporal variations in vertical stratification of the troposphere. An approximate model assuming a linear relationship between topography and interferometric phase has been used to correct observations with success in a few studies. Here, we present a robust approach to estimating the transfer function, K, between topography and phase that is relatively insensitive to confounding processes (earthquake deformation, phase ramps from orbital errors, tidal loading, etc.). Our approach takes advantage of a multiscale perspective by using a band-pass decomposition of both topography and observed phase. This decomposition into several spatial scales allows us to determine the bands wherein correlation between topography and phase is significant and stable. When possible, our approach also takes advantage of any inherent redundancy provided by multiple interferograms constructed with common scenes. We define a unique set of component time intervals for a given suite of interferometric pairs. We estimate an internally consistent transfer function for each component time interval, which can then be recombined to correct any arbitrary interferometric pair. We demonstrate our approach on a synthetic example and on data from two locations: Long Valley Caldera, California, which experienced prolonged periods of surface deformation from pressurization of a deep magma chamber, and one coseismic interferogram from the 2007 Mw 7.8 Tocapilla earthquake in northern Chile. In both examples, the corrected interferograms show improvements in regions of high relief, independent of whether or not we pre-correct the data for a source model. We believe that most of the remaining signals are predominately due to heterogeneous water vapor distribution that requires more sophisticated correction methods than those described here.

Rapid strain accumulation on the Ashkabad fault (Turkmenistan) from atmosphere‐corrected InSAR

“…They noted systematic differences between the two estimates of delay over the seaward and landward slopes of Mount Lebanon and suggested that the empirical method could not model stationary meteorological effects. A similar approach can also be applied at multiple scales, to identify and remove components of interferograms that correlate with topography across a variety of lengthscales [Shirzaei and Bürgmann, 2012;Lin et al, 2010]. However, all of these methods are susceptible to overcorrection of the data if elevation is correlated with the tectonic signal.…”

Correcting InSAR Topographically Correlated Tropospheric Delays Using a Power Law Model Based on ERA-Interim Reanalysis

“…Figure 4 shows the flow chart of the PLE method on the interferogram. The PLE method can account for lateral variations in space by estimating K m in multiple windows and can be applied in regions without removing a preliminary deformation [33]. The robust estimation technique is always available in each study area for a given day at a closet SAR acquisition.…”

“…Therefore, the selection of the band filter is not always trivial, as it requires empirical information about multi-scale dependent spectrums. However, we took advantage of the fact that the tropospheric signal is present at all wavelength scales to estimate the scaled factor from a spatial frequency band that was relatively insensitive to the other signals [33]. Similar to the original power law method [35,36], band filtering was applied to the phase and topography to select an appropriate band such that other phase contributions were negligible.…”

“…K is the scaled factor that needs to be estimated and φ c represents a constant shift that is applied to the entire interferogram. Several techniques in linear models have been developed to separate the tropospheric signals from residual orbits, deformation signals, or other phase noises, such as removal of a preliminary estimate of the deformation signals [31,32], evaluation of a local phase-topography relationship by spatial band-filtering that is insensitive to deformation signals [33], and spatially variable consideration for a piecewise slope correction over multiple windows [34]. The relationship between phase and topography using such empirical methods, however, depends on the spatial extent of the SAR scene, which sometimes leads to wrong estimates of spatial variation in the tropospheric stratification [26].…”

First Results from Sentinel-1A InSAR over Australia: Application to the Perth Basin

“…The success of this approach typically relies upon prior knowledge of either the location or spatial wavelength of deformation [62], of which we have neither in the Perth Basin. Predictive methods use external datasets, such as large-scale weather models [58,63] or GPS [64,65], to calculate and remove atmospheric artefacts.…”